People write books for specific reasons, and understanding those reasons can help you understand a book as a whole. So why did Luke write his Gospel? What was his purpose?
Consider a contrast: John’s Gospel was written with what you could call an evangelistic purpose, where the “good news” is about how to be individually born again. John explained his goals in John 20:31:
but these are written that you may believe that Jesus is the Christ, the Son of God, and that believing you may have life in His name (John 20:31).
Pay attention to John’s “that you may.” John wrote his Gospel to readers “that you may believe,” which implies they did not yet believe, and “that believing you may have life in His name,” which implies they did not yet have everlasting life (John 20:30-31). To believe and to have. That’s why we can say that John’s Gospel is evangelistic: it tells unbelievers what to do in order to have everlasting life (i.e., they must believe in Jesus).
In contrast to John, why did Luke write his Gospel? Here is what he writes:
it seemed good to me also, having had perfect understanding of all things from the very first, to write to you an orderly account, most excellent Theophilus, that you may know the certainty of those things in which you were instructed (Luke 1:3-4, emphasis added).
People had written about Jesus before. However, despite the existence of “many” other accounts (1:1), Luke saw the need for an orderly account of what happened with Jesus. Why? So that Theophilus may know the certainty of those things in which he was instructed. Theophilus had been instructed about Jesus. The Greek is katēcheō, from which English derives the words catechism, or to catechize, i.e., “to instruct by asking questions, receiving answers, and offering explanations and corrections” (Webster 1828). Medieval and Reformation churches had very developed programs of catechetical instruction for inquirers and new believers. It often took up to three years of regular instruction before a candidate (the catechumen) was permitted to be water baptized and afterward, to partake of the Lord’s Supper (or Communion). Some commentators see that structure already implied in Luke. But I think it would be a mistake to read that later development into Theophilus’ experience of being instructed, especially given how quickly people could be baptized in the Acts period (cf. Acts 8:36). In Acts 21:21, the same word is used for the misguided rumors that were being spread about Paul: “but they have been informed [katēchēthēsan] about you that you teach all the Jews who are among the Gentiles to forsake Moses, saying that they ought not to circumcise their children nor to walk according to the customs.”
Theophilus had been instructed about Jesus, but to what extent? We do not know. Whatever the case, Luke thought Theophilus would benefit from a more orderly account of Jesus’ acts and teachings, one that would give him certainty (asphaleia) about what he had been instructed. Just as John’s intended readers lacked both faith and life, Theophilus lacked that certainty. But what kind of certainty is this? BDAG says that asphaleia refers to a “stability of idea or statement” (BDAG, p. 147). Elsewhere, in Acts, Luke uses it to refer to a “securely” shut prison (Acts 5:23). It is not that Theophilus was a doubter instead of a believer. It is that he was a believer who needed to reinforce the foundations of his faith.
Have you ever heard several people tell stories about the same event, in slightly different ways, giving different details, and a different “take,” so that while you believed the event happened, you were fuzzy about how all the different details fit together? That might have been Theophilus’ experience in hearing about Jesus. He heard many accounts of Jesus. Much of what he heard was probably true, but perhaps with all the false gospels, myths, and foolish genealogies going around (cf. Titus 3:9), not to mention the gnostic and docetic teachings that were gaining ground (see Marshall, Luke, p. 40), Luke saw a pastoral need for a fully researched, logically ordered, and historically verified account of Jesus’ life.
Hence, several commentators have suggested that, while John’s Gospel has an evangelistic purpose, Luke’s Gospel, along with its sequel, the Book of Acts, has a quasi-apologetic purpose. Luke wrote to help new believers who have received some instruction about Jesus to gain a more stable and orderly understanding of His words and actions, especially how He fulfilled the OT prophecies (cf. Luke 1:1). Luke did not write to evangelize unbelievers but to promote certainty and stability among believers.